By taking , you get the solution , where is a constant. (Is that right? I hope I didn't mess up the calculations..)

However, , where are constants is also a valid solution, but it doesn't fit in the form that you obtained. So, using that method, you don't arrive to all the solutions. Just thought I'd point that out, I know that's not what you asked..

By taking , you get the solution , where is a constant. (Is that right? I hope I didn't mess up the calculations..)

However, , where are constants is also a valid solution, but it doesn't fit in the form that you obtained. So, using that method, you don't arrive to all the solutions. Just thought I'd point that out, I know that's not what you asked..

Here's my final general solution:

, how is it I'm missing a solution, the does not get included due to there being no in the original question :S

Well, actually you have. You wouldn't have had, if what I understood was right. Which, as it seems, is not. I simply didn't (and still don't) get what you meant when you said "set ", but since you arrived at this: